Mathematics
Te Tari Pāngarau me te Tatauranga
Department of Mathematics & Statistics

Upcoming seminars in Mathematics

Research seminars
Seminars in Statistics
Image reconstruction and unique continuation properties

Leo Tzou

University of Sydney

Date: Tuesday 11 June 2019
Time: 11:00 a.m.
Place: Room 241, 2nd floor, Science III building

A classical result of Jerison-Kenig showed that the optimal assumption for unique continuation properties for elliptic PDE. In this talk we will explore its connection to image reconstruction with impedance tomography. We will develop an analogous theory in the context of partial data inverse problems to obtain the same sharp regularity assumption as Jerison-Kenig. The method we use involves explicit microlocal construction of the Dirichlet Green's function which on its own may be of interest for partial data image reconstruction.

190529141321
Condorcet Domains Satisfying Arrow's Single-Peakedness

Arkadii Slinko

Department of Mathematics. University of Auckland

Date: Tuesday 9 July 2019
Time: 2:00 p.m.
Place: Room241, 2nd floor, Science III building

Condorcet domains are sets of linear orders with the property that, whenever the preferences of all voters belong to this set, the majority relation of any profile with an odd number of voters is transitive. Maximal Condorcet domains historically have attracted a special attention. We study maximal Condorcet domains that satisfy Arrow's single-peakedness which is more general than Black's single-peakedness. We show that all maximal Black's single-peaked domains on the set of m alternatives are isomorphic but we found a rich variety of maximal Arrow's single-peaked domains. We discover their recursive structure, prove that all of them have cardinality 2^{m-1}, and characterise them by two conditions: connectedness and minimal richness. We also classify Arrow's single-peaked Condorcet domains for up to 5 alternatives.

190626143334